Functional Models for Complex and High-Dimensional Data

功能数据分析的创新方法促进了对纵向研究、电子商务在线竞标、基因组研究、(生物)人口学和许多其他社会科学、生物和物理科学问题领域的数据分析的改进。所提出的功能方法提供了高度灵活的方法来表征这些数据，特别是研究它们的时间动态方面。研究人员将功能数据分析的适用范围扩展到该框架中未被广泛考虑的数据结构。这包括点过程、高维(大p，小n)数据以及出现在纵向和重复测量数据中的稀疏观测随机过程。特别是对于高维的非功能和点过程数据，功能数据分析方法具有导致变革性改进的潜力，而不仅仅是增量改进。研究人员开发了用于函数回归和相关的灵活的泛函和变系数模型。目前的建模方法受到太多的限制，不能广泛适用，需要更通用的模型。同样，曲线翘曲的分区最近也有了很大的发展，但仍然有许多重要的开放问题需要研究。研究人员将理论分析、模拟和数据应用相结合来进行这项研究，并将这些方法应用于电子商务、生物人口学、纵向研究和基因表达的数据。研究人员开发的统计方法立即适用于基因组学、人口学和生物人口学中的大型和复杂数据的分析。这些新的分析工具属于功能数据分析领域，旨在更好地理解依赖时间的过程。这些现象包括各种常见的现象，如生长、老化、在线拍卖期间的竞价，或反复观察到反复发生的事件，如哮喘发作。研究人员开发的方法阐明了这些现象的潜在动力学。这些方法的应用尤其有助于深入了解衰老和长寿的机制、在线拍卖的动态以及电子商务的其他实例。研究人员进一步扩展了这些方法的范围，例如，基于受试者基因表达谱的记录，对特定风险的改进预测变得可行。

Innovative methodology for Functional Data Analysis facilitates improved data analysis for longitudinal studies, e-commerce online bidding, genomic studies, (bio)demography and many other areas of the social, biological and physical sciences problems. The proposed functional approaches provide highly flexible ways to characterize such data, and especially to study their time-dynamic aspects. The investigator extends the applicability of Functional Data Analysis to data structures that have not been widely considered within this framework. This includes point processes, high-dimensional (large p, small n) data and sparsely observed stochastic processes as they occur in longitudinal and repeated measurements data. Especially for high-dimensional non-functional and point process data, Functional Data Analysis approaches have the potential to lead to transformative rather than merely incremental improvements. The investigator develops flexible functional and varying-coefficient models for functional regression and correlation. Current modeling approaches are too restrictive to be of broad applicability and more general models are needed. Similarly, the subarea of curve warping has seen much development lately but there remain many important open questions to be investigated. The investigator combines theoretical analysis, simulations, and data applications to conduct this research and applies the methods to data from e-commerce, biodemography, longitudinal studies and gene expression.The investigator develops statistical methodology that is immediately useful for the analysis of large and complex data in genomics, demography and biodemography. These new analysis tools, which fall into the field of Functional Data Analysis, are geared towards gaining a better understanding of time-dependent processes. These include a variety of commonly observed phenomena such as growth, aging, bidding during an online auction, or repeated observations of a recurring incident such as an asthma attack. The methods developed by the investigator elucidate the underlying dynamics of such phenomena. Application of these methods in particular enables insights into the mechanisms of aging and longevity, the dynamics of on-line auctions, and other instances of e-commerce. The investigator extends the scope of these methods further such that for example improved prediction of specific risks becomes feasible, based on a recording of a subject's gene expression profile.